Most employers would find it unacceptable to watch pornography in the workplace, according to the Education Secretary Justine Greening, who said it is important to have “high standards” in public life.

Mr Green, who serves as First Secretary of State, is the Prime Minister’s closest ally in Downing Street and vehemently denies he either watched or downloaded porn on his work computer almost a decade ago.

On Friday, the former Scotland Yard detective Neil Lewis told the BBC he was involved in analysing the then opposition immigration spokesperson’s computer during a police investigation into Home Office leaks.

He said that although “you can’t put fingers on a keyboard”, a number of factors meant that he was sure it was Mr Green himself who was accessing the “thumbnail” images.

“The computer was in Mr Green’s office, on his desk, logged in, his account, his name,” said Mr Lewis.

Asked on the BBC’s Andrew Marr Show whether it was OK to watch porn at work, Ms Greening replied: “Well, there are clear laws. I think most employers would say it wasn’t acceptable.”

But asked whether there was a “police vendetta” against her colleague, the Cabinet minister said the police needed to consider any steps in the wake of the leaks from the former detectives.

“I think there are two parts to this,” she said. “One is the Cabinet Office review into the behaviour of Damian Green and secondly, I think, any steps the police need to be taking in relation to what would seem to be a breach of police professionalism, in breaching privacy.

Ms Greening declined to comment directly on the investigation into Mr Green, but added: “I think it is important that we have high standards in public life.”

The allegations levelled against Mr Green echoed claims made by former Metropolitan Police Assistant Commissioner Bob Quick, who went public last month with his account of material discovered during an investigation into Home Office leaks.

On Sunday, the Health Secretary Jeremy Hunt added he has “confidence” in and “absolutely” trusts Mr Green.

Speaking on ITV’s Peston On Sunday, he said: “I do have confidence in Damian Green and I have actually been in a situation Damian Green was in, where you are in the eye of a storm and everyone thinks you’ve done an absolutely terrible thing and what I learnt from that is that you have to wait until an investigation is completed.

“And I was vindicated at the end of that process in my own case but I think we have to allow the Cabinet Office to complete their investigation.

“I know Damian Green as a colleague and I trust him absolutely and that’s why I believe what he says, but there is an investigation… and I think… we should wait.”

Dominic Grieve, a senior Tory MP and former Attorney General, also came to the defence of the embattled cabinet minister. “This can’t be right,” he told BBC’s Newsnight. “They are in flagrant breach of their own code of conduct and practice.”

He continued: “It has the smack of the police state about it. I find it very worrying. We give the police powers that other people do not have. They are not and must not be allowed to abuse those powers.”

Friends of Mr Green said they were “gobsmacked” by the allegations from the former detective and “outraged” at the BBC for broadcasting them.

Speaking to reporters outside his home in Kent on Friday, the Cabinet minister said: “I have maintained all along and I still maintain – it is the truth – that I did not download or look at pornography on my computer, but obviously while the investigation is going on I can’t say anymore.”

Ms Greening also cast doubt on Donald Trump’s anticipated visit to Britain next year, adding that his retweets of the far-right organisation, Britain First, “don’t particularly make any such visit a positive one”.

Echoing the words of the Prime Minister in relation to the incendiary social media posts, the Education Secretary said: “I think he was wrong to make those retweets. And I of course think Britain First is a group that is beyond the pale.